Examples showing how to rebin data to produce a smaller or bigger array without (and with) using interpolation. 

== Example 1 ==
Here we deal with the simplest case where any desired new shape is valid and no interpolation is done on the data to determine the new values.
 * First, floating slices objects are created for each dimension.
 * Second, the coordinates of the new bins are computed from the slices using mgrid.
 * Then, coordinates are transformed to integer indices.
 * And, finally, 'fancy indexing' is used to evaluate the original array at the desired indices.

{{{#!python
def rebin( a, newshape ):
        '''Rebin an array to a new shape.
        '''
        assert len(a.shape) == len(newshape)

        slices = [ slice(0,old, float(old)/new) for old,new in zip(a.shape,newshape) ]
        coordinates = mgrid[slices]
        indices = coordinates.astype('i')   #choose the biggest smaller integer index
        return a[tuple(indices)]
}}}

If we were only interested in reducing the sizes by some integer factor then we could use:
{{{#!python
def rebin_factor( a, newshape ):
        '''Rebin an array to a new shape.
        newshape must be a factor of a.shape.
        '''
        assert len(a.shape) == len(newshape)
        assert not sometrue(mod( a.shape, newshape ))

        slices = [ slice(None,None, old/new) for old,new in zip(a.shape,newshape) ]
        return a[slices]
}}}

== Example 2 ==
Here is an other way to deal with the reducing case for ndarrays. This acts identically to IDL's rebin command where all values in the original array are summed and divided amongst the entries in the new array. As in IDL, the new shape must be a factor of the old one.
The ugly 'evList trick' builds and executes a python command of the form

a.reshape(args[0],factor[0],).sum(1)/factor[0]
a.reshape(args[0],factor[0],args[1],factor[1],).sum(1).sum(2)/factor[0]/factor[1]

etc.
This general form is extended to cover the number of required dimensions.

{{{#!python
def rebin(a, *args):
    '''rebin ndarray data into a smaller ndarray of the same rank whose dimensions
    are factors of the original dimensions. eg. An array with 6 columns and 4 rows
    can be reduced to have 6,3,2 or 1 columns and 4,2 or 1 rows.
    example usages:
    >>> a=rand(6,4); b=rebin(a,3,2)
    >>> a=rand(6); b=rebin(a,2)
    '''
    shape = a.shape
    lenShape = len(shape)
    factor = asarray(shape)/asarray(args)
    evList = ['a.reshape('] + \
             ['args[%d],factor[%d],'%(i,i) for i in range(lenShape)] + \
             [')'] + ['.sum(%d)'%(i+1) for i in range(lenShape)] + \
             ['/factor[%d]'%i for i in range(lenShape)]
    print ''.join(evList)
    return eval(''.join(evList))
}}}

The above code returns an array of the same type as the input array. If the input is an integer array, the output values will be rounded down. If you want a float array which correctly averages the input values without rounding, you can do the following instead.

a.reshape(args[0],factor[0],).mean(1) [[BR]]
a.reshape(args[0],factor[0],args[1],factor[1],).mean(1).mean(2)

{{{#!python
def rebin(a, *args):
    shape = a.shape
    lenShape = len(shape)
    factor = asarray(shape)/asarray(args)
    evList = ['a.reshape('] + \
             ['args[%d],factor[%d],'%(i,i) for i in range(lenShape)] + \
             [')'] + ['.mean(%d)'%(i+1) for i in range(lenShape)]
    print ''.join(evList)
    return eval(''.join(evList))
}}}

Some test cases:
{{{#!python
# 2-D case
a=rand(6,4)
print a
b=rebin(a,6,4)
print b
b=rebin(a,6,2)
print b
b=rebin(a,3,2)
print b
b=rebin(a,1,1)

# 1-D case
print b
a=rand(4)
print a
b=rebin(a,4)
print b
b=rebin(a,2)
print b
b=rebin(a,1)
print b
}}}


== Example 3 ==
A python version of congrid, used in IDL, for resampling of data to arbitrary sizes, using a variety of nearest-neighbour and interpolation routines.

{{{#!python
import numpy as n
import scipy.interpolate
import scipy.ndimage

def congrid(a, newdims, method='linear', centre=False, minusone=False):
    '''Arbitrary resampling of source array to new dimension sizes.
    Currently only supports maintaining the same number of dimensions.
    To use 1-D arrays, first promote them to shape (x,1).
    
    Uses the same parameters and creates the same co-ordinate lookup points
    as IDL''s congrid routine, which apparently originally came from a VAX/VMS
    routine of the same name.

    method:
    neighbour - closest value from original data
    nearest and linear - uses n x 1-D interpolations using
                         scipy.interpolate.interp1d
    (see Numerical Recipes for validity of use of n 1-D interpolations)
    spline - uses ndimage.map_coordinates

    centre:
    True - interpolation points are at the centres of the bins
    False - points are at the front edge of the bin

    minusone:
    For example- inarray.shape = (i,j) & new dimensions = (x,y)
    False - inarray is resampled by factors of (i/x) * (j/y)
    True - inarray is resampled by(i-1)/(x-1) * (j-1)/(y-1)
    This prevents extrapolation one element beyond bounds of input array.
    '''
    if not a.dtype in [n.float64, n.float32]:
        a = n.cast[float](a)
    
    m1 = n.cast[int](minusone)
    ofs = n.cast[int](centre) * 0.5
    old = n.array( a.shape )
    ndims = len( a.shape )
    if len( newdims ) != ndims:
        print "[congrid] dimensions error. " \
              "This routine currently only support " \
              "rebinning to the same number of dimensions."
        return None
    newdims = n.asarray( newdims, dtype=float )    
    dimlist = []

    if method == 'neighbour':
        for i in range( ndims ):
            base = n.indices(newdims)[i]
            dimlist.append( (old[i] - m1) / (newdims[i] - m1) \
                            * (base + ofs) - ofs )
        cd = n.array( dimlist ).round().astype(int)
        newa = a[list( cd )]
        return newa
    
    elif method in ['nearest','linear']:
        # calculate new dims
        for i in range( ndims ):
            base = n.arange( newdims[i] )
            dimlist.append( (old[i] - m1) / (newdims[i] - m1) \
                            * (base + ofs) - ofs )
        # specify old dims
        olddims = [n.arange(i, dtype = n.float) for i in list( a.shape )]

        # first interpolation - for ndims = any
        mint = scipy.interpolate.interp1d( olddims[-1], a, kind=method )
        newa = mint( dimlist[-1] )

        trorder = [ndims - 1] + range( ndims - 1 )
        for i in range( ndims - 2, -1, -1 ):
            newa = newa.transpose( trorder )

            mint = scipy.interpolate.interp1d( olddims[i], newa, kind=method )
            newa = mint( dimlist[i] )

        if ndims > 1:
            # need one more transpose to return to original dimensions
            newa = newa.transpose( trorder )

        return newa
    elif method in ['spline']:
        oslices = [ slice(0,j) for j in old ]
        oldcoords = n.ogrid[oslices]
        nslices = [ slice(0,j) for j in list(newdims) ]
        newcoords = n.mgrid[nslices]

        newcoords_dims = range(n.rank(newcoords))
        #make first index last
        newcoords_dims.append(newcoords_dims.pop(0))
        newcoords_tr = newcoords.transpose(newcoords_dims)
        # makes a view that affects newcoords

        newcoords_tr += ofs        

        deltas = (n.asarray(old) - m1) / (newdims - m1)
        newcoords_tr *= deltas

        newcoords_tr -= ofs

        newa = scipy.ndimage.map_coordinates(a, newcoords)
        return newa
    else:
        print "Congrid error: Unrecognized interpolation type.\n", \
              "Currently only \'neighbour\', \'nearest\',\'linear\',", \
              "and \'spline\' are supported."
        return None 
}}}
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